A Lyapunov-Krasovskii Stability Analysis for Game-Theoretic Based Power Control in Optical Networks

We analyze the stability of a game-theoretic based power control algorithm for optical networks in the presence of time-delays. The control objective is to achieve optimal optical signal to noise ratio (OSNR) values for the signal channels. The control algorithms regularly adjust the signal powers entering the network based on a game-theoretic model. Each signal power is modeled as a player, whose goal is to maximize its own utility function. The utility function increases with an increasing OSNR value, and hence requires an increasing signal power. The trade-off is that if one player increases its OSNR value, this adversely affects the OSNR values of all of the other players. In addition to the signal powers, a dynamic price parameter is fed back to the power control algorithms. Time-delay is present for both the channel pricing parameter and the OSNR feedbacks in the network. We study the stability of the closed loop, time-delay system. The work utilizes singular perturbation theory modified to handle Lyapunov-Krasovskii techniques.